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arXiv · 2401.17780

A Policy Gradient Primal-Dual Algorithm for Constrained MDPs with Uniform PAC Guarantees

Toshinori Kitamura·Tadashi Kozuno·Masahiro Kato·Yuki Ichihara·Soichiro Nishimori·Akiyoshi Sannai·Sho Sonoda·Wataru Kumagai·Yutaka Matsuo
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Abstract

We study a primal-dual (PD) reinforcement learning (RL) algorithm for online constrained Markov decision processes (CMDPs). Despite its widespread practical use, the existing theoretical literature on PD-RL algorithms for this problem only provides sublinear regret guarantees and fails to ensure convergence to optimal policies. In this paper, we introduce a novel policy gradient PD algorithm with uniform probably approximate correctness (Uniform-PAC) guarantees, simultaneously ensuring convergence to optimal policies, sublinear regret, and polynomial sample complexity for any target accuracy. Notably, this represents the first Uniform-PAC algorithm for the online CMDP problem. In addition to the theoretical guarantees, we empirically demonstrate in a simple CMDP that our algorithm converges to optimal policies, while baseline algorithms exhibit oscillatory performance and constraint violation.

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Toshinori Kitamura, Tadashi Kozuno, Masahiro Kato, Yuki Ichihara, Soichiro Nishimori, Akiyoshi Sannai, Sho Sonoda, Wataru Kumagai, Yutaka Matsuo. 2024-01-31. A Policy Gradient Primal-Dual Algorithm for Constrained MDPs with Uniform PAC Guarantees. https://arxiv.org/abs/2401.17780

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